OVERNIGHT_NOTES: log post-gym session additions

Six new commits while Dane was at the gym, logged at top of the
doc: PJ-validity halfspace, reach tube overlays (your 4 points
done), polytopic barrier attempt, SOS polynomial barrier (degree-4,
CSDP OPTIMAL), Tikhonov bound derivation, controller-ref mismatch
finding.

Top of the file still has the blocked remote-push note with the
exact commands to unblock.  All work local on main; reading order
for morning: OVERNIGHT_NOTES -> journal.pdf (38 pages) ->
individual file headers.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

OVERNIGHT_NOTES.md

@@ -28,6 +28,52 @@ All work is committed locally; no data lost.
 Read this first when you open the laptop. Full details in
 `journal/journal.pdf` (newest entry: `2026-04-20-overnight-prompt-jump.tex`).
 
+## Post-gym session additions (2026-04-21 afternoon)
+
+Six more commits landed after you left for the gym. Headlines:
+
+6. **PJ-validity halfspace added to predicates.** New
+   `prompt_critical_margin_heatup` row in `safety_limits`: requires
+   `T_c ≥ T_c0 - 32.5` to guarantee `ρ ≤ 0.5·β` under the heatup
+   feedback-lin controller. Conjoined into `inv1_holds`. Now the PJ
+   approximation's validity is *part of the safety obligation* the
+   reach proves, not an external premise. (Your point 1.)
+
+7. **T_c + T_h + T_cold tube overlay plots.** Four-panel figures for
+   operation and heatup PJ: temperature tubes on one axis,
+   ΔT_core = T_h − T_cold as power proxy (MW right-axis), ρ
+   envelope in dollars, n envelope. See
+   `docs/figures/reach_operation_tubes.png` and
+   `docs/figures/reach_heatup_pj_tubes.png`. (Your point 4.)
+
+8. **Polytopic barrier check (naive):** fails as expected. Safety
+   polytope too big for LQR to contract from everywhere. Right tool
+   is Blanchini pre-image iteration; sketched in the script +
+   journal.
+
+9. **SOS polynomial barrier: FIRST SUCCESS.** Degree-4 polynomial
+   `B(x1, x2)` certifies safety on the 2-state reduced operation
+   projection. CSDP returned OPTIMAL. Full coefficients in the
+   journal entry. `code/scripts/barrier_sos_2d.jl`. This is the
+   non-quadratic barrier the plant needs; quadratic Lyapunov can
+   never work due to anisotropy, polynomial-of-degree-4 can.
+
+10. **Tikhonov bound derivation for PJ.** Wrote out the
+    singular-perturbation theorem application: puts the PKE in
+    slow-fast form, identifies `n_PJ(x)` as the quasi-steady
+    manifold, and shows error is `O(Λ) = O(10⁻⁴)` uniformly after
+    the boundary layer. Rigorous rate. The `prompt_critical_margin_heatup`
+    invariant is the validity hypothesis, which reach discharges.
+    Empirical 0.1% error and the bound are consistent. Remaining
+    gap: compute the problem-specific constant `C` numerically.
+
+11. **Controller-ref mismatch found in heatup tube plots.** With
+    `X_entry` at `T_c ∈ [285, 291]` but controller ref starting at
+    `T_standby = 275`, the FL controller commands cooling (ρ stays
+    negative). Captured in journal as an apass for next session;
+    physics-grade fix is to parameterize `ref.T_start` from current
+    `T_c` at mode entry.
+
 ## TL;DR
 
 1. **Implemented the prompt-jump (singular-perturbation) PKE reduction**